Thermodynamics of supercooled liquid silicon and its glass transition
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Thermodynamics of supercooled liquid silicon and its glass transition
Caetano R. Miranda and Alex Antonelli Instituto de Fisica “Gleb Wataghin”, Universidade Estadual de Campinas, CP 6165, CEP 13083-970, Campinas, SP, Brazil
ABSTRACT
The thermodynamic properties of various phases of silicon, namely, crystalline, amorphous, and liquid, have been studied using the Reversible Scaling method within Monte Carlo simulations. The recently proposed Environment Dependent Interatomic Potential was employed to model the atomic interactions. The calculated Gibbs free energy and entropy of both crystalline and liquid phases are in good agreement with available experimental data. The glass transition is continuous, taking place at 1150 K. We have also determined the Kauzmann temperature, TK = 955 K , the thermodynamic fragility, F3 4 = 0.64 , which indicates a fragile thermodynamic character to l-Si, and the configurational entropy of the amorphous phase, Sconf ≈ 1.2 k B atom .
INTRODUCTION
The behavior of supercooled liquids and their glass transition constitute one of the most interesting unsolved problems in condensed matter physics [1-2]. Although silicon is one of the most studied materials, the behavior of its supercooled liquid and its glass transition still remain not completely understood and controversial. Primarily because the amorphous phase of silicon cannot be attained through quench of the liquid. The cooling rates available in the laboratory are not fast enough to prevent crystallization. The transition amorphous/liquid was studied twenty years ago using amorphous silicon, obtained via ion implantation, and fast laser-heating technique [3], indicating that the melting of amorphous silicon would be a first-order transition. Such fast heating rates are necessary to prevent the recrystallization of the amorphous phase. In face of these experimental difficulties the use of computer simulations became an invaluable tool for the study of these phenomena. In this work, we present a quantitative study, through computer simulations, of the thermodynamics of silicon in its various phases, with special focus on its glass transition. In this case, the liquid phase is cooled down below the melting point (supercooled liquid), eventually undergoing a glass transition. The full understanding of the thermodynamic properties of a physical system requires the knowledge of the free energy and the entropy, which are particularly difficult to attain from computer simulations, in contrast with other properties such as enthalpy, volume, pressure, etc, which are readily obtained in any computer simulation. This difficulty stems from the fact that free energy and entropy depend on the total volume in phase space available to the system. We have used in our study the recently proposed Reversible Scaling method within Monte Carlo
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simulations (RS-MC) [4]. Thermodynamic properties of this metastable phase as well as those for crystalline and liquid phases have been obtained. This study of free energy and entropy allo
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